OMCC 2002 Problem 3

For every integer $a>1$ an infinite list of integers is constructed $L(a)$ , as follows:

[list] $a$ is the first number in the list $L(a)$ .[/list] [list] Given a number $b$ in $L(a)$ , the next number in the list is $b+c$ , where $c$ is the largest integer that divides $b$ and is smaller than $b$ .[/list] Find all the integers $a>1$ such that $2002$ is in the list $L(a)$ .